In preparing this new edition of Principia Mathematica, the authors have thought it best to leave the text unchanged, except as regards misprints and minor errors, even where they were aware of possible improvements. The chief reason for this decision is that any alteration of the propositions would have entailed alteration of the references, which would have meant a very great labour. It seemed preferable, therefore, to state in an introduction the main improvements which appear desirable. Some of these are scarcely open to question; others are, as yet, a matter of opinion.

The most definite improvement resulting from work in mathematical logic during the past fourteen years is the substitution, in Part I, Section A, of the one indefinable “p and q are incompatible” (or, alternatively, “p and q are both false”) for the two indefinables “not-p” and “p or q.” This is due to Dr H. M. Sheffer. Consequentially, M. Jean Nicod showed that one primitive proposition could replace the five primitive propositions *1·2·3·4·5·6.

From this there follows a great simplification in the building up of molecular propositions and matrices; *9 is replaced by a new chapter, *8, given in Appendix A to this Volume.

Another point about which there can be no doubt is that there is no need of the distinction between real and apparent variables, nor of the primitive idea “assertion of a propositional function.”